

from math import factorial







class 					__lowercase  :





							"""simple docstring"""

							def __init__(					self    ,						__UpperCAmelCase    ,						__UpperCAmelCase						)		->       Optional[int]:
														A      :					Union[str, Any]      		=					real
														if isinstance(__UpperCAmelCase    ,						__UpperCAmelCase						):
																					A      :					str      		=					[1] * rank
														else:
																					A      :					Dict      		=					rank




							def __repr__(					self						)		->       List[str]:
														return (
														    f'{self.real}+'
														    f'{"+".join(str(__UpperCAmelCase						)+"E"+str(n+1						)for n,dual in enumerate(self.duals						)						)}'
														)




							def       snake_case			(					self						)		->       Union[str, Any]:
														A      :					List[Any]      		=					self.duals.copy()
														while cur[-1] == 0:
																					cur.pop(-1						)
														return Dual(self.real    ,						__UpperCAmelCase						)




							def __add__(					self    ,						__UpperCAmelCase						)		->       Any:
														if not isinstance(__UpperCAmelCase    ,						__UpperCAmelCase						):
																					return Dual(self.real + other    ,						self.duals						)
														A      :					int      		=					self.duals.copy()
														A      :					Any      		=					other.duals.copy()
														if len(__UpperCAmelCase						) > len(__UpperCAmelCase						):
																					o_dual.extend([1] * (len(__UpperCAmelCase						) - len(__UpperCAmelCase						))						)
														elif len(__UpperCAmelCase						) < len(__UpperCAmelCase						):
																					s_dual.extend([1] * (len(__UpperCAmelCase						) - len(__UpperCAmelCase						))						)
														A      :					List[str]      		=					[]
														for i in range(len(__UpperCAmelCase						)						):
																					new_duals.append(s_dual[i] + o_dual[i]						)
														return Dual(self.real + other.real    ,						__UpperCAmelCase						)

							UpperCAmelCase_						:		int								=	__add__




							def __sub__(					self    ,						__UpperCAmelCase						)		->       List[str]:
														return self + other * -1




							def __mul__(					self    ,						__UpperCAmelCase						)		->       List[str]:
														if not isinstance(__UpperCAmelCase    ,						__UpperCAmelCase						):
																					A      :					Union[str, Any]      		=					[]
																					for i in self.duals:
																												new_duals.append(i * other						)
																					return Dual(self.real * other    ,						__UpperCAmelCase						)
														A      :					Optional[Any]      		=					[0] * (len(self.duals						) + len(other.duals						) + 1)
														for i, item in enumerate(self.duals						):
																					for j, jtem in enumerate(other.duals						):
																												new_duals[i + j + 1] += item * jtem
														for k in range(len(self.duals						)						):
																					new_duals[k] += self.duals[k] * other.real
														for index in range(len(other.duals						)						):
																					new_duals[index] += other.duals[index] * self.real
														return Dual(self.real * other.real    ,						__UpperCAmelCase						)

							UpperCAmelCase_						:		int								=	__mul__




							def __truediv__(					self    ,						__UpperCAmelCase						)		->       Optional[int]:
														if not isinstance(__UpperCAmelCase    ,						__UpperCAmelCase						):
																					A      :					Optional[Any]      		=					[]
																					for i in self.duals:
																												new_duals.append(i / other						)
																					return Dual(self.real / other    ,						__UpperCAmelCase						)
														raise ValueError




							def __floordiv__(					self    ,						__UpperCAmelCase						)		->       Union[str, Any]:
														if not isinstance(__UpperCAmelCase    ,						__UpperCAmelCase						):
																					A      :					List[Any]      		=					[]
																					for i in self.duals:
																												new_duals.append(i // other						)
																					return Dual(self.real // other    ,						__UpperCAmelCase						)
														raise ValueError






							def __pow__(					self    ,						__UpperCAmelCase						)		->       Any:
														if n < 0 or isinstance(__UpperCAmelCase    ,						__UpperCAmelCase						):
																					raise ValueError('''power must be a positive integer'''						)
														if n == 0:
																					return 1
														if n == 1:
																					return self
														A      :					Dict      		=					self
														for _ in range(n - 1						):
																					x *= self
														return x






def        snake_case__		(    lowerCamelCase_     ,				lowerCamelCase_     ,				lowerCamelCase_		):
							if not callable(lowerCamelCase_		):
														raise ValueError('''differentiate() requires a function as input for func'''		)
							if not isinstance(lowerCamelCase_     ,				(float, int)		):
														raise ValueError('''differentiate() requires a float as input for position'''		)
							if not isinstance(lowerCamelCase_     ,				lowerCamelCase_		):
														raise ValueError('''differentiate() requires an int as input for order'''		)
							A      :					Any      		=					Dual(lowerCamelCase_     ,				1		)
							A      :					Dict      		=					func(lowerCamelCase_		)
							if order == 0:
														return result.real
							return result.duals[order - 1] * factorial(lowerCamelCase_		)


if __name__ == "__main__":
		import doctest

		doctest.testmod()






		def        snake_case__		(    lowerCamelCase_		):
									return y**2 * y**4

		print(differentiate(f, 9, 2))









import os
import unittest

from huggingface_hub.utils import are_progress_bars_disabled

import transformers.models.bart.tokenization_bart
from transformers import logging
from transformers.testing_utils import CaptureLogger, mockenv, mockenv_context
from transformers.utils.logging import disable_progress_bar, enable_progress_bar







class 					__lowercase  (						unittest.TestCase				):





							"""simple docstring"""

							def       snake_case			(					self						)		->       Union[str, Any]:
														A      :					Dict      		=					logging.get_logger()

														# the current default level is logging.WARNING
														A      :					List[Any]      		=					logging.get_verbosity()

														logging.set_verbosity_error()
														self.assertEqual(logger.getEffectiveLevel()    ,						logging.get_verbosity()						)

														logging.set_verbosity_warning()
														self.assertEqual(logger.getEffectiveLevel()    ,						logging.get_verbosity()						)

														logging.set_verbosity_info()
														self.assertEqual(logger.getEffectiveLevel()    ,						logging.get_verbosity()						)

														logging.set_verbosity_debug()
														self.assertEqual(logger.getEffectiveLevel()    ,						logging.get_verbosity()						)

														# restore to the original level
														logging.set_verbosity(__UpperCAmelCase						)




							def       snake_case			(					self						)		->       str:
														A      :					Any      		=					logging.get_verbosity()

														A      :					Optional[Any]      		=					logging.get_logger('''transformers.models.bart.tokenization_bart'''						)
														A      :					Tuple      		=					'''Testing 1, 2, 3'''

														# should be able to log warnings (if default settings weren't overridden by `pytest --log-level-all`)
														if level_origin <= logging.WARNING:
																					with CaptureLogger(__UpperCAmelCase						) as cl:
																												logger.warning(__UpperCAmelCase						)
																					self.assertEqual(cl.out    ,						msg + '''\n'''						)

														# this is setting the level for all of `transformers.*` loggers
														logging.set_verbosity_error()

														# should not be able to log warnings
														with CaptureLogger(__UpperCAmelCase						) as cl:
																					logger.warning(__UpperCAmelCase						)
														self.assertEqual(cl.out    ,						''''''						)

														# should be able to log warnings again
														logging.set_verbosity_warning()
														with CaptureLogger(__UpperCAmelCase						) as cl:
																					logger.warning(__UpperCAmelCase						)
														self.assertEqual(cl.out    ,						msg + '''\n'''						)

														# restore to the original level
														logging.set_verbosity(__UpperCAmelCase						)




							@mockenv(TRANSFORMERS_VERBOSITY='''error'''						)
							def       snake_case			(					self						)		->       Optional[int]:
														# reset for the env var to take effect, next time some logger call is made
														transformers.utils.logging._reset_library_root_logger()
														# this action activates the env var
														A      :					int      		=					logging.get_logger('''transformers.models.bart.tokenization_bart'''						)

														A      :					Any      		=					os.getenv('''TRANSFORMERS_VERBOSITY'''    ,						__UpperCAmelCase						)
														A      :					List[str]      		=					logging.log_levels[env_level_str]

														A      :					Optional[int]      		=					logging.get_verbosity()
														self.assertEqual(
														    __UpperCAmelCase    ,						__UpperCAmelCase    ,						f'TRANSFORMERS_VERBOSITY={env_level_str}/{env_level}, but internal verbosity is {current_level}'    ,						)

														# restore to the original level
														A      :					str      		=					''''''
														transformers.utils.logging._reset_library_root_logger()




							@mockenv(TRANSFORMERS_VERBOSITY='''super-error'''						)
							def       snake_case			(					self						)		->       Optional[int]:
														# reset for the env var to take effect, next time some logger call is made
														transformers.utils.logging._reset_library_root_logger()
														A      :					str      		=					logging.logging.getLogger()
														with CaptureLogger(__UpperCAmelCase						) as cl:
																					# this action activates the env var
																					logging.get_logger('''transformers.models.bart.tokenization_bart'''						)
														self.assertIn('''Unknown option TRANSFORMERS_VERBOSITY=super-error'''    ,						cl.out						)

														# no need to restore as nothing was changed






							def       snake_case			(					self						)		->       Optional[int]:
														# testing `logger.warning_advice()`
														transformers.utils.logging._reset_library_root_logger()

														A      :					Union[str, Any]      		=					logging.get_logger('''transformers.models.bart.tokenization_bart'''						)
														A      :					Optional[int]      		=					'''Testing 1, 2, 3'''

														with mockenv_context(TRANSFORMERS_NO_ADVISORY_WARNINGS='''1'''						):
																					# nothing should be logged as env var disables this method
																					with CaptureLogger(__UpperCAmelCase						) as cl:
																												logger.warning_advice(__UpperCAmelCase						)
																					self.assertEqual(cl.out    ,						''''''						)

														with mockenv_context(TRANSFORMERS_NO_ADVISORY_WARNINGS=''''''						):
																					# should log normally as TRANSFORMERS_NO_ADVISORY_WARNINGS is unset
																					with CaptureLogger(__UpperCAmelCase						) as cl:
																												logger.warning_advice(__UpperCAmelCase						)
																					self.assertEqual(cl.out    ,						msg + '''\n'''						)






def        snake_case__		(    ):
							disable_progress_bar()
							assert are_progress_bars_disabled()

							enable_progress_bar()
							assert not are_progress_bars_disabled()






